for example, if you are putting together a regression equation for a problem, and it calls for a one percent decline, how do you know wether to use .01 or 1?

A couple tips:

First, keep in mind what a coefficient is: it denotes how many units your DV will change with a one UNIT change in an IV. If you units happen to be in percentage points, then it simply means that a one percentage point (i.e. 5% to 6%) in the IV predicts a beta unit change in the DV.

However, if you have log-transformed variables, you will need to consider percentage (versus percentage point/unit change). If you have logged variables (aka log-log or log-linear models), you will interpret coefficients to mean that a one percent change in the IV predicts a beta percent change in the DV. This ignores special cases where only the DV or the IV is logged, but the logic is the same.

For example, say the DV is ROE as a percentage.

If it states that the IV unit, say, CapEx, is denominated in, say, percentage of sales, then you should use the former case (e.g. if CapEx/Sales increases from 25% to 26% then ROE increases by “beta” units, perhaps from 1% to 2%).

If both sides were log-transformed, then it would be a 1% increase in the underlying ratio predicts a beta percent change in ROE. If beta=1, then this would indicate that CapEx/Sales and ROE are perfectly elastic, meaning they change together in the same way over all ranges. In the former case, a 1 percentage point change in CapEx from 25% to 26% (a four percent change) predicts a 1 percentage point change in ROE from 1% to 2% (a one hundred percent change). In this case, a one percent change predicts a one percent change over the entire range.

In any event you should always consider your underlying units and what makes logical sense. The problems should spell out how the units are denominated. Rule of thumb is that if it says “X%” think units and “X% change” or anything that is logged to percentage change. And if you get a weird logical result, like a $1 (vs, say, $1MM or $1MMM) increase in something indicates a X% change in the DV, you need to re-look at your units.

wow, thanks!